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This monograph on the description and study of representations of the rotation group of three-dimensional space and of the Lorentz group features advanced topics and techniques crucial to many areas of modern theoretical physics. Prerequisites include a familiarity with the differential and integral calculus of several variables and the fundamentals of linear algebra. Suitable for advanced undergraduate and graduate students in mathematical physics, the book is also designed for mathematicians studying the representations of Lie groups, for whom it can serve as an introduction to the general theory of representation.The treatment encompasses all the basic material of the theory of representations used in quantum mechanics. The two-part approach begins with representations of the group of rotations of three-dimensional space, analyzing the rotation group and its representations. The second part, covering representations of the Lorentz group, includes an exploration of relativistic-invariant equations. The text concludes with three helpful supplements and a bibliography.

The authors of this book were Soviet mathematicians with expertise especially in mathematical physics.

Prefatory Note Preface Part I: Representations of the Group of Rotations of Three-Dimensional SpaceChapter I: The Rotation Group and Its RepresentationsSections 1-6Chapter II: Further Analysis of the Representations of the Rotation GroupSections 7-10 Part II: Representations of the Lorentz GroupChapter I: The Lorentz Group and Its RepresentationsSections 1-6Chapter II: Relativistic-Invariant EquationsSections 7-11 SupplementsI-III Bibliography